Supercell design for first-principles simulations of solids and application to diamond, silica, and superionic water

For efficient first-principles computation of crystalline materials at high density and temperature, an optimal choice of the supercell is important to minimize finite size errors. An algorithm is presented to construct compact supercells for arbitrary crystal structures. Rather than constructing standard supercells by replicating the conventional unit cell, we employ the full flexibility that we gain by using arbitrary combinations of the primitive cell vectors in order to construct a series of cubic and nearly cubic supercells. In cases where different polymorphs of a material needed to be compared, we are able construct supercells of consistent size. Our approach also allows us to efficiently study the finite size effects in systems like superionic water where they would otherwise difficult to obtain because a standard replication of the unit cells leads to supercells that are too expensive to be used for first-principles simulations. We apply our method to simple, body-centered, and face-centered cubic as well as hexagonal close packed cells. We present simulation results for diamond, silica in the pyrite structure, and superionic water with an face-centered cubic oxygen sub-lattice. The effects of the finite simulation cell size and Brillouin zone sampling on the computed pressure and internal energy are analyzed.